Overview

Controlling invasive predators at a national scale. Modelling and communicating the complex factors enabling native prey to persist in the face of environmental variability and predation by invasive predators.

Managers commonly carry out spatially intensive control programs for extended jurations of time to reduce introduced species abundance and allow native species to regenerate and establish breeding populations, (e.g. poison baiting and trapping of fox control to protect rock-wallabies [@kinnear1988; @hone1999].

Key points this introduction will cover:

  1. To reduce the risk of unexpected outcomes, a combined modelling and experimental approach can clarify the outcomes of invasive species control (Ogle 2009).

  • Previous research has attempted to characterize the interactions between species and resources (Choquenot & Ruscoe 2000).

  • And simulation studies have attempted this… (Tompkins et al. 2006; 2013)

  1. Computational framework is vital to this……

  2. Statistical software such as JAGS (Plummer 2010), WinBUGS (Suess & Trumbo 2010) and STAN (STAN development Team 2015) in combination with increasing computational power has allowed these advance (Ogle 2009).

Hypotheses, key questions, objectives, predictions etc etc

In this thesis I will use observed data to build ecosystem models that allow researchers to directly quantify the interactions among invasive species (Peng 2015).

  1. To build a research synthesis database of the theoretical relationships proposed in over 100 years of conservation research in NZ and the experimental work supporting these models. We need a uniform set of models and notation to develop from (e.g. Holland et al. 2015; Ruscoe et al. 2005; Choquenot & Ruscoe 2000; Ruscoe et al. 2004; King et al. 2003).

  2. Use a combined theoretical modelling and experimental approach to clarify the outcomes of invasive species control in three large-scale ecological datasets (Chapters 2,3,4). I build and test previous research that has attempted to characterize these interactions between invasive species, resources and native species in New Zealand Forests (Choquenot & Ruscoe 2000 + +).

  3. Advances in ecological modelling tools have opened up opportunities to assess and parameterize theoretical models from observational data (King 2012). Along with this comes the correct partitioning of observation and process error. We use statistical software such as JAGS (Plummer 2010), WinBUGS (Suess & Trumbo 2010) and STAN (STAN development Team 2015) to develop the understanding of how these sources of error may effect the goals and targets of conservation managers and researchers alike.

This is the template that can be used to build ucdown and is also the draft sections of my PhD thesis.

For this template I have divided the “chapters” into key sections needed to build and troubleshoot bookdown for graduate research projects. The aim of this bookdown is to provide a working archive of code for the bookdown package use with the statistics network.

You can reference chapters like so:

  • Chapter @ref(intro)

  • Chapter @ref(methods)

  • Chapter @ref(literature)

… check out the website for more resources here

Framework

To build a research synthesis database of the theoretical relationships proposed in over 100 years of conservation research in NZ and the experimental work supporting these models. We need a uniform set of models and notation to develop from (e.g. Holland et al. 2015; Ruscoe et al. 2005; Choquenot & Ruscoe 2000; Ruscoe et al. 2004; King et al. 2003).

  • The introduction aims to use reproducible meta-data tools…

I will address these questions using the following data studies.

Computational framework is vital to this……

General concepts approached throughout this PhD are viewed through a Bayesian philosophy. I use this method to develop three different, but equally important foundations of modern science; reproducibility (framework), novel model application (analysis) and predicted management implications (results and application). The aim of this framework was to create a feedback loop for transparent community research with sound reproducibility and replicability at a national scale (New Zealand wide; Figure 1).

image-20200512194955116

image-20200513140157797

image-20200513140157797

Package tidyPipes

My PhD is build around a similar approach to the tidyverse view. Theoretically, all the work laid out here is not unusual or uncommon. The unique aspect of this thesis is that I have conceptualise this into a general approach to reproducible research that extended in the current literature (cite) to create a approach I have defined as tidyPipes (figure below).

image-20200513140211137

image-20200513140211137

Reproducible framework

[publication: Davidson2020-Reproducibility]

Reproducible approaches to replicate theoretical scenarios provide the framework to account for changes in such unanticipated and complex outcomes

  • to be simulated under a range of simple interactions which have produced sometimes
  • complex and unexpected outcomes between predators, prey and competing species (e.g. Caut et al. 2009; Courchamp et al. 2003; Courchamp et al. 2000; Caut et al. 2007).
  • Theoretical models provide insight into the range of possible effects we might observe, but these models need to be tested using data from real ecosystems to evaluate their validity.
  • Additionally, larger inhabited islands and continental systems may consist of more interacting species, that in turn may increase the likelihood of observing these sorts of unexpected outcomes following invasive species removal (e.g. Ruscoe et al. 2011).

General scientific process

Aim

Dealing with Reproducibility Why and how to make a reproducible workflow for invasive species research in New Zealand

This chapter creates a workflow that allows the ability to access and use the invasive species database in a reproducible way…. Etc etc

Importance of reproducibility between community groups etc

We also conduct a meta-analysis to shows that even though the time it takes to reproduce a workflow comes back THIS>…

  • Citation records (Google scholar and elsivear)
  • Collaborations (international vs domestic)
  • Outreach (twitter/fb).

Layout

Equation structure (Stage vs age)

vs

Mathematical approach (Differential vs difference)

vs

Statistical method (Frequentist vs. Bayesian)

What do you think are the key references for these levels?

Ecosystem (top down and bottom up forces)

Community (pest species, subset of ecosystem)

Population (single species in population)

Individual (each unit in population)

An old process

Is this why data science split off?

I began my PhD work focused on understanding the population dynamics of interacting pest species in New Zealand forests. The focus of this work was to address the two questions:

Work-flow diagram

Literature review

[publication: Davidson2020-Invasive species database]

I estimate the effects of predator control from these models but addionationally provide a reproducible workflow in systems with and without stoat control, varying control methods and differences in resources flow between these systems (Chapter Four).

I did this by simulationously developing models for estimating the collected data on food availailiy and abundance of species in the same systems. I did this in a applied Bayesian approach.

I use this understanding to forecast the likely effects of species removals on the objectives set by the government of New Zealand under “Predator Free New Zealand 2050” (Chapter Five).

This thesis focuses on transperantly collecting and reproducing the previously constructed ecological models that describe the population dynamics of the four main invasive species of interacting mammals (stoats, possums, rats and mice) in New Zealand forests. These species are also the main targets of PFNZ2050 (Chapter Six).

Aligning this ecological research with good research practise that insures the results are reproducible and replicable by allowing open access to statistical code and analysis is vital for any targeted solution to PFNZ2050 (Chapter 7).

I have developed the understanding derived from these models to predict the effects of management manipulations and reduce the likelihood of unanticipated outcomes.

knitr::include_graphics("./img/jones2016.png", auto_pdf = TRUE)

New Zealand has a long history of conservation research (Cite??) and Islands ecosystems have been the focus of both observational and experimental manipulation

  • For example, the increase in mesopredators after the removal of invasive cats on Little Barrier Island (New Zealand; (Rayner et al. 2007),
  • the effect of the brown treesnake (Boiga irregularis) on frugivorous bird species and the forest structure on Gaum (Rogers et al. 2017) and,
  • the role of ship rats (Rattus rattus) and mice (Mus musculus) on Surprise Island, New Caledonia (Courchamp et al. 2011; Caut et al. 2009).

We have done so much work but even the visual diagrams are different….

  • As time changes but also methods and practises
  • But there should at least be a constant notation for NZPF?
  • Why is notation correct?
  • total number of species etc in NZ

Theoretical scenarios provide the framework for such unanticipated and complex outcomes

  • to be simulated under a range of simple interactions which have produced sometimes
  • complex and unexpected outcomes between predators, prey and competing species (e.g. Caut et al. 2009; Courchamp et al. 2003; Courchamp et al. 2000; Caut et al. 2007).
  • Theoretical models provide insight into the range of possible effects we might observe, but these models need to be tested using data from real ecosystems to evaluate their validity.
  • Additionally, larger inhabited islands and continental systems may consist of more interacting species, that in turn may increase the likelihood of observing these sorts of unexpected outcomes following invasive species removal (e.g. Ruscoe et al. 2011).

What are others asking for??

  • Use of bayes in Ecology….
  • Importance of prior choices
  • Needs reproducibility
  • ecosystem modification.

PFNZ2050

  • PFNZ 2050….
  • We do this by ==
  • In combination with these sorts of unexpected outcomes of predator control (cite) managers must also allocate funding and resources that are restricted by funding and other anthropological drivers (cite).
  • While historically the focus of threatened species management has been on the vulnerability of native biota, this PhD aims to shift this focus from vulnerability to persistence with an emphasis on enhancing species strengths (persistence in the environment) not weaknesses (vulnerability to threats).
  • For managers and in particular, leaders of PFNZ2050 (cite) will need to communicate and untiles nation-wide community groups to successfully manage invasive species in NZ native forests and nationally into the future.
  • Little is known about the complex multi-species dynamics of established pest populations in ecosystems on mainland New Zealand and Australia.
  • This PhD project will investigate these interactions using multi-species modelling using existing data on the abundance, survival and persistence of native biota (e.g. Ruscoe et al. 2011, Ruscoe et al. 2012, J Griffiths unpublished data) in predator-removal experiments.

But this is not an impossible target:

  • Nevertheless, globally, conservation and management groups can refer to a large corpus of scientific and government projects with successful reductions and eradications of invasive species (cite)
  • Including large reviews and meta-analysis of complex control and eradication programs
  • However, none of these research projects can single handily conclude that the target species should be removed or even predict with confidence, the expected impact on the surrounding areas.
  • Indirect ecological responses from other species, most often when top predators are removed are blamed (Rayner et al. 2007; Courchamp et al. 1999; Courchamp et al. 2011; Ruscoe et al. 2011).
  • But are there other aspects of the research corpus that lead to unexpected consequences of invasive species

Examples (maybe of contradicting outcomes from same studies):

  • The removal of wolves (top predator) in Yellowstone National park lead to trophic cascades, and the subsequent re-introduction has restored interactions between key species within the park (Smith et al. 2003; Fortin et al. 2005; Barber-Meyer 2015).
  • In the reverse application of this issue, the deliberate removal of top predators through pest control of cats on Macquarie Island highlighted negative issues with the increase of a mesopredator (rats; Bergstrom et al. 2009).
  • The removal of dingoes (the top predator in many Australian ecosystems) appears to allow fox and cat populations (mesopredators) to increase in abundance (Glen & Dickman 2005).
  • It is common practice for organisations to control these populations (Gurevitch & Padilla 2004; Clavero & Garcia-Berthou 2005).
  • But the scale, intensity and timing of programs vary hugely, between each studies key questions and outcomes (Figure 1).
A simple diagramatical representation of key differences in modelling population dynamics of invasive species

A simple diagramatical representation of key differences in modelling population dynamics of invasive species

What happens when it gets big??

Theoretical scenarios provide the framework for such unanticipated and complex outcomes - to be simulated under a range of simple interactions which have produced sometimes - complex and unexpected outcomes between predators, prey and competing species (e.g. Caut et al. 2009; Courchamp et al. 2003; Courchamp et al. 2000; Caut et al. 2007). - Theoretical models provide insight into the range of possible effects we might observe, but these models need to be tested using data from real ecosystems to evaluate their validity. - Additionally, larger inhabited islands and continental systems may consist of more interacting species, that in turn may increase the likelihood of observing these sorts of unexpected outcomes following invasive species removal (e.g. Ruscoe et al. 2011).

How can temporal, spatial and genetic variation effect the outputs of studies
  • Differences in the models, theory and methods across similar environments lead to generalisations to control varying from a particular theory. These generalisationsd drive the targets of predator control but oftern multiple theorotical explainations would lead to fundemental differences in future developments of control programs.

PF2050?

  • Phd focus

Using CR models

Complex models

Communcation tools

A key factor = breakthrough for PF2050…

Reproducibility

Tools to do this:

This PhD approaches applied ecology and bayesian modelling as a future solution to human based island wide cntrol using community groups and national level tech develpment.

Just a sample isn’t it??

# Define some sample data
data <- list(a=1000, b=800, c=600, d=400)

DiagrammeR::grViz("
digraph graph2 {

graph [layout = dot]

# node definitions with substituted label text
node [shape = rectangle, width = 4, fillcolor = Biege]
a [label = '@@1']
b [label = '@@2']
c [label = '@@3']
d [label = '@@4']

a -> b -> c -> d

}

[1]:  paste0('Raw Data (n = ', data$a, ')')
[2]: paste0('Remove Errors (n = ', data$b, ')')
[3]: paste0('Identify Potential Customers (n = ', data$c, ')')
[4]: paste0('Select Top Priorities (n = ', data$d, ')')
")

Background

What defined the database:

  • This is an important question when insure the use and longevity of the project

  • Databases that exist

New Zealand plant database

Overall this chapter will present the literature review (systematic)

  • Numerical and functional responses

  • Model type

  • Data needed…

  • Resource for community groups and scientists alike

  • To the extent that New Zealand has developed an inter……

  • With mixed responses….

image-20191230154755433

image-20191230154755433

In this thesis I have used observational data

  1. Statistical software such as JAGS (Plummer 2010), WinBUGS (Suess & Trumbo 2010) and STAN (STAN development Team 2015) in combination with increasing computational power has allowed these advance (Ogle 2009).

We conducted a systematic review to idenifity all invasive species in NZ currently documented.

  • we did this using figure 1:

Collection of NZ invasive mammal species present currently (2020)

  • a generic conceptual model for all of the possible interactions and environment types in NZ. Something like below:

Language choices

  • Invasive (either native or introduced??)

  • Introduced (pre?? Dog and Kiore examples…)

  • Native (NZ birds)

  • Invaders

  • Alien species

    • alien species are second to habitat loss… [@wilcove1998]

Modelling choices

  • Functional and numerical responses…
  • Observations and Processes
  • Invidividual, Population and community
  • Stochastic and deterministic
  • Temporial and Enviromental
  • Genetics?
  • Demographic stochasticity
  • Estimation or Prediction..

Bayesian Modelling

  • Why?

  • Bias?

  • incorperate proirs

  • Reproducibility is key

  • Approach to creating a reproducible workflow

    1. What exactly does a scientist do? (FLow diagram)
    2. Making packages to make these steps more transperent
    3. REsulting repositorys to do this (containerizations>>!)

Aim

Invasive species database A database (DB) for invasive species in New Zealand (NZ)

Creating a database of research to understand the current knowledge of observation and/or population level demographics of New Zealand invasive species.

NOTE: This is already part of a standard literature review and if this does not get any further than that it is a bonus.

Methods

Accounting for researcher bias … with reproducibility

Data

Defining a set of parameters for a meta-analysis of invasive mammals in NZ.

List of animals

<- table generator-> <- blog on this!!!->

What are the unexpected outcomes of predator removal globally using New Zealand as a case study.

To test the theoretical relationships proposed in over 100 years of conservation research we need a uniform get of models and notation to develop from.

This thesis deseminates the current published literature from the scientific literature using a reproducible approach.

Collect results of published literature of predator removal, again using New Zealand as a case study

I create the first open-source database of pest control models using this dataset.

Describe a combined modelling and experimental approach that could clarify the outcomes of invasive species control (Ogle 2009).

Previous research has attempted to characterize the interactions between species and resources (Choquenot & Ruscoe 2000).

Both numerical and functional responses have been proposed to describe invasive species processes in NZs temperate forest.

Simulation studies have attempted this… (Tompkins et al. 2006; 2013)

Create a computationally reproducible framework

We use observed data to build ecosystem models that allow researchers to directly quantify the interactions among invasive species (Peng 2015).

Both numerical and functional responses for species have been shown to explain some of the population dynamics observed in New Zealand temperate forests (e.g. Holland et al. 2015; Ruscoe et al. 2005; Choquenot & Ruscoe 2000; Ruscoe et al. 2004; King et al. 2003).

Advances in ecological modelling tools have opened up opportunities to assess and parameterize theoretical models from observational data (King 2012).

Both continuous and discrete capture-recapture models have been proposed

A state-space framework for a generalised modelling approach to the three main target pests for PFNZ2050

Managers commonly carry out spatially intensive control programs for extended jurations of time to reduce introduced species abundance and allow native species to regenerate and establish breeding populations, (e.g. poison baiting and trapping of fox control to protect rock-wallabies [@kinnear1988; @hone1999].

Statistical Methods

  • Bayesian hierarchical modelling

Software

Key linking packages to make this work:

  • Revtools

  • Scholar

  • Python?

Results

New Zealand mixed native forests

For example: 3rd chapter…

Population demography focuses on the dynamics of populations and the drivers of these dynamics.

  • population hard to define
  • density

Results

Discussion

There I have created a group of datasets and code that will allow me to extend on this for future publications/thesis chapters. Options I see with current structure:

  • Compare multiple beech datasets

  • Compare different modelling approaches

  • any other ideas

Parameter identifiablity

  • This is when, given perfect data (e.g a infinite number of samples) it is possible estimate the true values of the parameters

  • This is often difficult to assess and more often researchers settle for estimability, which is when, given the data, the approx. parameter is a unique estimate.

  • Quality of parameter estimates can be assessed using:

  • variability of estimates over repeated measures (variance)

  • difference between estimate (\(\hat{y}\)) and true value also know as the mean squared error (MSE, bias)

  • Auger-Methe and colleages say that parameter estimability within linear Gaussian SSMs is a general issue. Parameter idenedifiability is even more difficult to understand.

The orginal theory [@gompertz1825]

References

Undocumented References

Spatz, D. R., Zilliacus, K. M., Holmes, N. D., Butchart, S. H. M., Genovesi, P., Ceballos, G., … Croll, D. A. (2017). Globally threatened vertebrates on islands with invasive species. Science Advances, 3(10), e1603080. https://doi.org/10.1126/sciadv.1603080

“Gompertz B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of Lon- don B: Biological Sciences. 1825; 182:513–85.”

“Verhulst P-F. Notice sur la loi que la population suit dans son accroissement. Correspondance mathe´- matique et physique. 1938; 10:113–21.”

THEY ARE:

3.Winsor CP. The Gompertz curve as a growth curve. Proc. Nat. Acad. Sci. 1932; 18(1):1–8. PMID: 16577417

  1. Laird AK. Dynamics of tumor growth. British Journal of Cancer. 1964; 18:490–502.

  2. Ricker WE. Growth rates and models. In: Hoar WS, Randall DJ, Brett JR, editors. Fish physiology. Lon- don: Academic Press; 1979. p. 677–743.

  3. Zwietering MH, Jongenburger I, Rombouts FM, Van’T Rie T K. Modeling of the bacterial growth Curve. Appl. Env. Micriobiol. 1990; 56(6):1975–81.

  4. Skinner GE, Larkin JW. Mathematical modeling of microbial growth: a review. Journal of Food Safety. 1994; 14:1975–217.

  5. Starck JM, Ricklefs RE. Avian growth and development. The evolution within the altricial-precocial spectrum. New York, Oxford: Oxford University Press; 1998. 441 p.

  6. Aggrey SE. Comparison of three nonlinear and sprline regression models for describing chicken growth curves. Poultry Science. 2002; 81:1782–8. PMID: 12512566

  7. Paine CET, Marthews TR, Vogt DR, Purves D, Rees M, Hector A, Turnbull LA. How to fit nonlinear plant growth models and calculate growth rates: and update for ecologists. Methods in Ecology and Evolution. 2012; 3:245–56.

  8. Benzekry S, Lamont C, Beheshti A, Tracz A, Ebos JML, Hlatky L, Hahnfeldt P. Classical mathematical models for description and prediction of experimental tumor growth. PLOS Computional Biology. 2014; 10(8): e1003800.

  9. Halmi MIE, Shukor MS, Johari WIW, Shuker MY. Evaluation of several mathematical models for fitting the growth of the algae Dunaliella tertiolecta. Asian Journal of Plant Biology. 2014; 2(1):1–6.